Problem-Solving Agents - Cal...

CPE/CSC 580-S06 Artificial Intelligence – Intelligent Agents

Problem-Solving Agents

Subclass of goal-based agents

goal formulation

problem formulation

example problems

• toy problems

• real-world problems

search

• search strategies

• constraint satisfaction

solution

Franz J. Kurfess, Cal Poly SLO 57


Goal Formulation

Specify the objectives to be achieved

goal

a set of desirable world states in which the

objectives have been achieved

current / initial situation

starting point for the goal formulation

actions

cause transitions between world states



Problem Formulation

Actions and states to consider

states possible world states

accessibility the agent can determine via its

sensors in which state it is

consequences of actions the agent knows the

results of its actions

levels problems and actions can be specified at

various levels

constraints conditions that influence the

problem-solving process

performance measures to be applied

costs utilization of resources



Example: vacuum world, restricted to two locations with two states(dirty, clean)



Problem Types

Not all problems are created equal

single-state problem

multiple-state problem

contingency problem

exploration problem



Single-State Problem

exact prediction is possible

state

is known exactly after any sequence of actions

accessibility of the world

all essential information can be obtained

through sensors

consequences of actions

are known to the agent

goal

for each known initial state, there is a unique

goal state that is guaranteed to be reachable via

an action sequence

simplest case, but severely restricted



Example: Vacuum world, [?]p. 58Limitations: Can’t deal with

incomplete accessibilityincomplete knowledge about consequenceschanges in the worldindeterminism in the world, in actions



Multiple-State Problem

semi-exact prediction is possible

state is not known exactly, but limited to a set of

possible states after each action


not all essential information can be obtained

through sensors

reasoning can be used to determine the set of

possible states


are not always or completely known to the

agent; actions or the environment might exhibit

randomness

goal due to ignorance, there may be no fixed action

sequence that leads to the goal

less restricted, but more complex



Example: Vacuum world, [?]p. 58, but the agent has no sensorsThe action sequence right, suck, left, suck is guaranteed to reach the goalstate from any initial state

Limitations: Can’t deal withchanges in the world during execution (“contingencies”)



Contingency Problem

exact prediction is impossible

state unknown in advance, may depend on the

outcome of actions and changes in the

environment


some essential information may be obtained

through sensors only at execution time


may not be known at planning time

goal instead of single action sequences, there are

trees of actions

contingency branching point in the tree of actions

agent design different from the previous two cases:

the agent must act on incomplete plans

search and execution phases are interleaved



Example: Vacuum world, [?]p. 58, The effect of a suck action is random.There is no action sequence that can be calculated at planning time and isguaranteed to reach the goal state.

Limitations: Can’t deal withsituations in which the environment or effects of action are unknown



Exploration Problem

effects of actions are unknown

state

the set of possible states may be unknown


some essential information may be obtained

through sensors only at execution time


may not be known at planning time

goal can’t be completely formulated in advance

because states and consequences may not be

known at planning time

discovery

what states exist

experimentation

what are the outcomes of actions

learning

remember and evaluate experimentsFranz J. Kurfess, Cal Poly SLO 64


agent design

different from the previous cases: the agent

must experiment

search

requires search in the real world, not in an

abstract model

realistic problems, very hard



Well-Defined Problems

exact formulation of problems and solutions

initial state

current state / set of states, or the state at the

beginning of the problem-solving process

must be known to the agent

operator

description of an action

state space

set of all states reachable from the initial state

by a possible sequence of actions

path in the search space

sequence of actions between two states

goal test

determines if the agent has reached a goal state

path cost

function that assigns a cost to a path

usually the sum of the costs of actions along



the path

data type problem

components: Initial-State, Operators,

Goal-Test, Path-Cost

solution

path from the initial state to a state that

satisfies the goal test

search algorithm

takes the problem data type and computes a

solution

basis for a formal treatment



Performance Measuring

for problem solving

success

Has a solution been found?

quality

Is it a good solution?

What are the criteria?

optimal solution

may be difficult to find and not necessary

cost

sum of

• search cost (time, resources to find a

solution)

• path cost (as defined above)



toy problems

vacuum world

8-queens

8-puzzle

missionaries and cannibals



Vacuum World

simplified version

two squares, either dirty or clean, vacuum has

sensors

states

location of vacuum, squares dirty or clean

operators

move left, move right, suck

goal test

all squares clean

path cost

1 unit per action



see Figure 3.2, 3.6 in [?], p. 66



8-Queens

no queen attacks any other

states

arrangement of 8 queens on the board

operators

add a queen

goal test

no queen attacked

path cost

zero (irrelevant, all solutions are equally good)

restrictions on the states and operators can lead to

vastly different search spaces



incremental version; complete-state formulation moves queens around[?]page 64



Real-World Problems

route finding

travel advisory, computer networks, airline travel

travelling salesperson

each city must be visited exactly once

more complex than route finding

VLSI layout

positioning of gates and connections

too complex for humans

crucial for successfull operation and costs

robot navigation

generalization of route finding to continuous

space, possibly multi-dimensional (actions

involving arms)



Search

Examine possible sequences of actions

input

problem description, initial state

output

solution as an action sequence

search space

set of all possible action sequences



Search

in Artificial Intelligence

search of a problem space

for a solution to a problem

not: search through data structures

basic idea:

find a path from the initial description of a

problem to a description of the solved problem

problem space is created incrementally,

not predefined and already in existence

problem-solving method

powerful technique for many different areas



Problem Space

Representation

Network

graph with nodes as states and arcs as possible

steps

unique representations of states, multiple

incoming arcs

Tree

multiple representations of states



Search

different ways to search

random search

next step is selected randomly from the possible

ones

non-systematic; can’t guarantee complete

coverage of the search space; paths may be

selected multiple times; may take infinite time

blind search

systematic approach; no knowledge about

closeness to the solution; complete coverage;

ineffective if closeness to solutions can be

measured

directed search

systematic approach; paths leading towards the

solution are preferred



Search Methods

used in AI problems

depth-first

blind, systematic

expands each path to the end, backtracking

when a dead end is encountered

breadth-first

blind, systematic

all nodes at one level are expanded

finds the shortest path

beam search

directed, heuristic variation of breadth-first

only a limited number of nodes are expanded

all successor nodes are evaluated, the best ones

are selected for expansion



hill-climbing

directed variation of depth-first

successor node with the greatest progress

towards the goal is selected

problems: local maxima, plateaus, ridges

branch and bound

directed search

most promising node in the tree is selected

finds the shortest path

problem: significant portion of the search tree

must be expanded

best-first

directed, heuristic search algorithm

requires estimate of the distance to the solution

selects the node with the smallest estimate

problem: does not take into account the length

of already expanded parts of the paths



A? (A-Star)

combination of best-first and branch and bound

requires estimate of the distance to the solution

uses estimate and previous path length to

calculate the cost

if estimates are always greater than zero but

never greater than the actual cost, the lowest

cost path will be found

reduces the number of nodes expanded by

best-first



Solution

Action sequence that satisfies the goal

validation

Does the solution really achieve the goal?

verification

Is the sequence of actions admissible?

feasibility

With the available resources, can the sequence

of actions be carried out?

execution

actions are carried out



Summary

Problem-Solving Agents

goal formulation

objectives that need to be achieved

problem formulation

actions and states to consider

problem types

single-/multiple state, contingency, exploration

example problems toy problems real-world

problems

search strategies

solution

execution of the action sequence


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